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Theorem setindel 4263
 Description: -Induction in terms of membership in a class. (Contributed by Mario Carneiro and Jim Kingdon, 22-Oct-2018.)
Assertion
Ref Expression
setindel
Distinct variable group:   ,,

Proof of Theorem setindel
StepHypRef Expression
1 clelsb3 2142 . . . . . . 7
21ralbii 2330 . . . . . 6
3 df-ral 2311 . . . . . 6
42, 3bitri 173 . . . . 5
54imbi1i 227 . . . 4
65albii 1359 . . 3
7 ax-setind 4262 . . 3
86, 7sylbir 125 . 2
9 eqv 3240 . 2
108, 9sylibr 137 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1241   wceq 1243   wcel 1393  wsb 1645  wral 2306  cvv 2557 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-setind 4262 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-ral 2311  df-v 2559 This theorem is referenced by:  setind  4264
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